Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process

Article Mathematics

Finite-Time Stability Analysis of Fractional Delay Systems

Ahmed M. Elshenhab et al.

Summary: This paper considers nonhomogeneous systems of fractional differential equations with pure delay and uses their solutions representation and delayed Mittag-Leffler matrix functions to obtain finite time stability results.

MATHEMATICS (2022)

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Article Mathematics

Controllability and Hyers-Ulam Stability of Differential Systems with Pure Delay

Ahmed M. Elshenhab et al.

Summary: This study considers dynamic systems of linear and nonlinear differential equations with pure delay. The representation of solutions using delayed Mittag-Leffler matrix functions is used for obtaining controllability and Hyers-Ulam stability results. Sufficient and necessary conditions for the controllability of linear delay differential systems are established by introducing a delay Gramian matrix. Additionally, sufficient conditions for controllability and Hyers-Ulam stability of nonlinear delay differential systems are derived by applying Krasnoselskii's fixed point theorem. These results improve, extend, and complement existing ones.

MATHEMATICS (2022)

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Article Mathematics

Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay

Ahmed M. Elshenhab et al.

Summary: This paper considers nonhomogeneous systems governed by second-order linear differential equations with pure delay. The exact solutions of these systems and their delayed matrix functions are used to obtain the finite-time stability results. Our results extend and improve some previous results by removing some restrictive conditions. An example is provided to illustrate our theoretical results.

MATHEMATICS (2022)

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Article Mathematics, Applied

Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

T. Sathiyaraj et al.

Summary: This paper investigates the controllability of second-order nonlinear stochastic delay systems driven by Rosenblatt distributions in finite dimensional spaces. The controllability conditions are established using fixed point theory, delayed sine and cosine matrices, and delayed Grammian matrices. The controllability results for these systems are illustrated through numerical simulations.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2021)

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Article Physics, Multidisciplinary

Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

Ravi P. Agarwal et al.

Summary: This paper explores the oscillation properties of fourth-order neutral differential equations by employing Riccati substitution and comparison techniques. New oscillation conditions are derived to ensure that all solutions of the equation are oscillatory. The results presented supplement existing knowledge on neutral differential equations and are illustrated with an example.

ENTROPY (2021)

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Article Mathematics, Applied

Representation of solutions for linear fractional systems with pure delay and multiple delays

Ahmed M. Elshenhab et al.

Summary: This study examines nonhomogeneous systems of linear fractional equations with pure delay and multiple delays, where the linear parts are given by permutable or nonpermutable matrices. Solutions are represented using delayed Mittag-Leffler type matrix functions and Laplace transform, presenting new results that build upon previous findings.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Mathematics, Applied

The Truncated Euler-Maruyama Method for Highly Nonlinear Neutral Stochastic Differential Equations With Time-Dependent Delay

Aleksandra Petrovic et al.

Summary: The paper establishes the Lq-convergence of the truncated Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay under the Khasminskii-type condition. The main result is illustrated by an example, and the appropriate results are given in the appendix for completeness. The entire consideration is influenced by the presence of the neutral term and delay function.

FILOMAT (2021)

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Article Mathematics, Applied